Problem: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$6.00$, and bags of cookies cost $$2.50$, and sales equaled $$41.50$ in total. There were $3$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6x+2.5y = 41.5}$ ${y = x+3}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+3}$ for $y$ in the first equation. ${6x + 2.5}{(x+3)}{= 41.5}$ Simplify and solve for $x$ $ 6x+2.5x + 7.5 = 41.5 $ $ 8.5x+7.5 = 41.5 $ $ 8.5x = 34 $ $ x = \dfrac{34}{8.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+3}$ to find $y$ ${y = }{(4)}{ + 3}$ ${y = 7}$ You can also plug ${x = 4}$ into $ {6x+2.5y = 41.5}$ and get the same answer for $y$ ${6}{(4)}{ + 2.5y = 41.5}$ ${y = 7}$ $4$ bags of candy and $7$ bags of cookies were sold.